Robust prescribed-time observer-based sliding mode control: Theoretical design and flight control applications

This paper proposes a prescribed-time observer-based sliding mode control law for nonlinear systems subject to external disturbances and internal variable dynamics. First, a prescribed-time extended-state-observer (PTESO) is designed by incorporating a trigonometric-time-scaling function. The PTESO achieves total disturbance compensation within a pre-assigned time, theoretically independent of initial conditions and parameter tuning. Then, by combining the proposed PTESO and the exponential-time-scaling function, a PTESO-based prescribed-time sliding mode (PTSM) control law is proposed, ensuring system states converge precisely as arbitrarily pre-specified. Furthermore, a practical implementation of the proposed control law is presented for a typical flight control application: roll stabilization of a bank-to-turn precision-guided flight vehicle. The PTESO-based PTSM control design fully leverages the prescribed-time convergence properties while effectively alleviates the peaking phenomenon. Finally, the simulations demonstrate that the proposed PTESO-based PTSM roll control law outperforms existing approaches in terms of prescribed-time convergence performance and robustness.